Mathematics: 9. nick has desigied a diamond-shaped kite as shown below. the measures of so me sides of the kite, are marked in the figure. find the value of x (justify)

OKAY!Step-by-step explanation:...

9. nick has desigied a diamond-shaped kite as shown

mercedes73

14.03.2022

$x=\frac{10\sqrt{6}}{7}\ in$

Step-by-step explanation:

step 1

In the right triangle DOC

Find the measure of side DO

Applying the Pythagoras Theorem

$DC^{2}=DO^{2}+OC^{2}$

substitute the given values

$7^{2}=DO^{2}+5^{2}$

$DO^{2}=7^{2}-5^{2}$

$DO^{2}=49-25$

$DO^{2}=24$

$DO=2\sqrt{6}\ in$

step 2

In the right triangle DOC

Find the sine of angle ∠ODC

sin(∠ODC)=OC/DC

substitute

sin(ODC)=5/7 -----> equation A

step 3

In the right triangle DOP

Find the sine of angle ∠ODP

sin(∠ODP)=OP/DO

substitute

$sin(ODP)=x/2\sqrt{6}$ -----> equation B

step 4

Find the value of x

In this problem

∠ODC=∠ODP

equate equation A and equation B

$5/7=x/2\sqrt{6}$

$x=\frac{10\sqrt{6}}{7}\ in$

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